The theory of nonlinear dynamics provides a basis for understanding and potentially controlling many complex physical and engineering systems. An extensive literature exists for nonlinear dynamics in the brain and related work (18). It is well known that brain waves exhibit seemingly random, unpredictable behavior, that is characteristic of deterministic chaos (1, 20). Moreover, chaotic behavior is "normal," while nonchaotic or periodic behavior is indicative of pathophysiology in experimental epilepsy (20). Schiff et al. (11) showed that chemically-induced seizures in rat-brain can be electrically controlled, leading to speculation (4) that human epilepsy may be controlled without drug or surgical intervention. However, effective use of chaos control for epilepsy requires definitive seizure prediction. Thus, this invention diagnoses brain wave data via chaotic time series analysis (CTSA) methods to predict an epileptic seizure.
Nonlinear analysis of neurological diseases via EEG data is extensive. For example, see the 1994 review by Elbert et al. (18). Epilepsy can be recognized only with clear EEG manifestations, but even these seizures are not easy to detect because there is no stereotyped pattern characteristic of all seizures (5). Work by Olsen and colleagues (7) used various linear measures with autoregressive modeling, discriminant analysis, clustering, and artificial neural networks. Valuable nonlinear tools for studying EEG data include correlation dimension, mutual information function, Kolmogorov entropy, phase-space attractors, and largest Lyapunov exponent. No publications or patents apply one or more CTSA measures to EEG data for systematic characterization of non-seizure, seizure, and transition-to-seizure, for prediction of an epileptic seizure.
Very recent analysis by Theiler (16) studied correlation dimension and Lyapunov exponent, using a form of surrogate analysis on a single EEG time series during an epileptic seizure. The surrogate analysis involved a random shuffling of blocks of time serial data, each block containing one quasi-periodic spike-wave complex. The auto-correlation function for the original data is nearly indistinguishable from the surrogate data. The correlation dimension for the original data is significantly different from the surrogate data only at large scale sizes and large embedding dimensions. The maximum Lyapunov exponent (.lambda.) was negative for both the original and surrogate data and not substantially different, contrary to previous work which found positive .lambda. values. Theiler concluded that his analysis suggests a nonlinear oscillator with noise on the time scale of the spike-wave complex, but cannot indicate whether chaos exits on a shorter time scale.